Ever wondered how far off a number is from the average? Thatโs exactly what a Z-score helps you figure out!
When you’re analyzing test scores, investment returns, or scientific data, a Z-score tells you how many standard deviations a value is from the mean.
This article breaks it down step by stepโwith the formula, real-life examples and a calculator to make it all crystal clear.
Table of Contents
๐ข Want to skip the math? Use the calculator belowโjust enter your value, the mean, and the standard deviation. We’ll calculate the Z-score instantly.
๐งฎ Z-Score Calculator
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๐โโ๏ธ What Is a Z-Score?
A Z-score (also called a standard score) shows how far a data point is from the mean (average) in terms of standard deviation.
It helps you understand whether a number is above or below average, and by how much.
If the Z-score is:
- 0 โ it’s right on the average
- Positive โ it’s above the average
- Negative โ it’s below the average
๐งพ Z-Score Formula
Hereโs the formula to calculate Z:
Z = (X - ฮผ) รท ฯWhere:
- X = your data point
- ฮผ (mu) = the mean
- ฯ (sigma) = the standard deviation
โ๏ธ Example
Letโs say you got a score of 85 on a test.
- The class average (mean) is 70
- The standard deviation is 10
Z = (85 - 70) รท 10 = 15 รท 10 = 1.5โ
Your Z-score is 1.5
That means your score is 1.5 standard deviations above the mean. Great job!
๐ Why Z-Score Matters
Z-scores are useful for:
- Grading on a curve
- Identifying outliers in data
- Comparing different data sets
- Assessing risk in finance
- Understanding normal distributions in science and stats
๐ก Pro Tips
- A Z-score between -2 and +2 is typically considered normal in many data sets
- Z-scores work best when the data is normally distributed (bell curve)
- You can convert Z-scores to percentiles using standard tables